Thank you for reporting, we will resolve it shortly
Q.
The magnitude of the magnetic induction at a point on the axis at a large distance $(r)$ from the centre of a circular coil of $'n'$ turns and area $'A'$ carrying current $(l)$ is given by
As we know that the magnetic field on the axis of a circular current carrying loop,
$B=\frac{\mu_{0} n I a^{2}}{2\left(r^{2}+a^{2}\right)^{3 / 2}}$...(i)
where, $I=$ current through the coil,
$a=$ radius of $a$ circular loop,
$r=$ distance of point from the centre along the axis
and $n=$ number of turns in the coil.
Area of the coil, $A=\pi a^{2}$
$\Rightarrow a^{2}=\frac{A}{\pi}$...(ii)
and it $r > >a$ then, $\left(r^{2}+a^{2}\right)^{3 / 2} \approx r^{3}$...(iii)
From Eqs. (i), (ii) and (iii), we get
$B =\left(\frac{\mu_{0} n I}{2 r^{3}}\right) \frac{A}{\pi} \times \frac{2}{2}$
$\Rightarrow B =\frac{2 \mu_{0} n I A}{4 \pi r^{3}}$
So, option (b) is correct.